Exponent Calculator
Free exponent calculator. Calculate powers (xⁿ), square roots, cube roots, and any nth root instantly with step-by-step working.
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Common Powers Quick Reference
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
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1. Exponents and Powers Explained
An exponent (or power) tells you how many times to multiply a base number by itself. The notation xⁿ means: multiply x by itself n times.
Examples: 2³ = 2 × 2 × 2 = 8. 10⁴ = 10 × 10 × 10 × 10 = 10,000. 5² = 25.
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2. Laws of Exponents
- Product rule: xᵃ × xᵇ = x^(a+b). Example: 2³ × 2⁴ = 2⁷ = 128.
- Quotient rule: xᵃ ÷ xᵇ = x^(a−b). Example: 3⁵ ÷ 3² = 3³ = 27.
- Power rule: (xᵃ)ᵇ = x^(a×b). Example: (2²)³ = 2⁶ = 64.
- Zero exponent: x⁰ = 1 (for any non-zero x).
- Negative exponent: x⁻ⁿ = 1/xⁿ. Example: 2⁻³ = 1/8.
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3. Square Roots and Cube Roots
Roots are the inverse of powers. √x = x^(1/2). ∛x = x^(1/3). Example: √144 = 12 because 12² = 144. ∛27 = 3 because 3³ = 27.
See also: Exponents & Powers Guide | Scientific Notation | Logarithm Calculator